CalcNotes0208-page11 - (Section 2.8: Continuity) 2.8.11...

(Section 2.8: Continuity) 2.8.11PART G: CONTINUITY THEOREMS AND EXAMPLESAlgebra of ContinuityIffand gare functions that are continuous at a, then so are the functions f+g, f±g, and fg. • The function fgis, also, if ga()±0. • The function fnis, also, if nis a positive integer. • The function fnis, also, if: • (nis an odd positive integer), or • (nis an even positive integer, and fa>0.) In a manner similar to the limit properties in Section 2.2, Part A, the theorem above, together with the fact that constant functions and the identity function (represented by fx=x) are everywhere continuous (on ±), justifies the following: Continuity of Rational FunctionsA rational function is continuous on its domain.

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